{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "03b7a3e5-1ac0-4a65-b187-f0255b2d244f",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "from tqdm import tqdm\n",
    "import time\n",
    "import seaborn as sns\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pylab as plt\n",
    "from scipy.interpolate import interp1d\n",
    "from scipy.special import ellipj\n",
    "from scipy.special import ellipkinc\n",
    "from scipy.special import ellipk\n",
    "from scipy.optimize import fsolve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "7fb739b4-4894-4616-bd92-a33a9779781a",
   "metadata": {},
   "outputs": [],
   "source": [
    "M = 1 # massa do BURACO negro\n",
    "b_c = 3*np.sqrt(3)*M # parametro de impacto CRITICO\n",
    "theta_0 = 80*np.pi/180. #angulo de visada do buraco negro"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "36c27287-e174-4fb7-a317-e1561e36b99d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def B_fun(p,M):\n",
    "    return (p**3/(p-2*M))**0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ee90cff3-0da8-49b0-9a51-f41254743d9f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def Q_fun(P,M):    \n",
    "    return ((P - 2*M)*(P+6*M))**0.5\n",
    "\n",
    "\n",
    "def gamma(alpha, theta_0):\n",
    "    a = np.cos(alpha)**2 + 1/(np.tan(theta_0)**(2))\n",
    "    return np.arccos( np.cos(alpha)/(a**0.5)  )\n",
    "\n",
    "\n",
    "def k2(P,M):\n",
    "   \n",
    "    Q = Q_fun(P,M)\n",
    "    return ((Q-P+6*M)/(2*Q))\n",
    "\n",
    "def zeta_inf(P,M):\n",
    "    Q = Q_fun(P,M)\n",
    "    ratio = (Q-P+2*M)/(Q-P +6*M)\n",
    "    return np.arcsin( ratio**0.5 )\n",
    "\n",
    "### 1st order\n",
    "def Up(P,alpha,M,theta_0): #u = 1/r\n",
    "    # b = np.sqrt(X**2 + Y**2)\n",
    "    # alpha = np.arctan(Y/X)\n",
    "    Q = Q_fun(P)\n",
    "    A1 = (Q-P+2*M)/(4*M*P)\n",
    "    A2 = (Q-P+6*M)/(4*M*P)\n",
    "    g = gamma(alpha,theta_0)\n",
    "    ratio = (Q/P)**0.5\n",
    "    mod = k2(P,M)\n",
    "    sn, cn, dn, ph = ellipj( ((g/2)*ratio + ellipkinc(zeta_inf(P) , mod)), mod )\n",
    "    \n",
    "    return -A1 + A2*sn**2 #tenho de procurar jacobi porra\n",
    "\n",
    "### 2nd order\n",
    "def Up2(P,alpha,M,theta_0): #u = 1/r\n",
    "    # b = np.sqrt(X**2 + Y**2)\n",
    "    # alpha = np.arctan(Y/X)\n",
    "    Q = Q_fun(P)\n",
    "    A1 = (Q-P+2*M)/(4*M*P)\n",
    "    A2 = (Q-P+6*M)/(4*M*P)\n",
    "    g = gamma(alpha,theta_0)\n",
    "    ratio = (Q/P)**0.5\n",
    "    mod = k2(P,M)\n",
    "    sn, cn, dn, ph = ellipj( (0.5*(g-2*np.pi)*ratio + 2*ellipk(mod) - ellipkinc(zeta_inf(P) , mod)), mod )\n",
    "    \n",
    "    return -A1 + A2*sn**2 #tenho de procurar jacobi porra"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "10de1187-cb91-4b61-8064-0732d88c9579",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "52it [01:15,  1.45s/it]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize = (8,8))\n",
    "r_list = np.arange(4,30,0.5)*M\n",
    "# r_list = [6,10,20,30]*M\n",
    "\n",
    "color=iter(plt.cm.hot_r(np.linspace(0.3 ,1.,  np.shape(r_list)[0])))\n",
    "\n",
    "for idx, r in tqdm(enumerate(r_list)):\n",
    "\n",
    "    #colors\n",
    "    c=next(color)\n",
    "\n",
    "    alpha_list = np.arange(0, 2*np.pi,0.01)\n",
    "    b_list = []\n",
    "    b_list2 = []\n",
    "    alpha_res = []\n",
    "    alpha_res2 = []\n",
    "    #plt.figure(figsize = (15,15), dpi = 300)\n",
    "    for alpha in alpha_list:    \n",
    "        # 1st order figure\n",
    "        def cu(P):\n",
    "            return 1 - r*Up(P,alpha)\n",
    "        \n",
    "        # 2nd order figure\n",
    "        def cu2(P):\n",
    "            return -(1 - r*Up2(P,alpha))\n",
    "        \n",
    "        \n",
    "        guess = b_c + 0.1\n",
    "        # raiz = fsolve(cu,[guess])[0]\n",
    "        raiz = fsolve(cu,[guess])[0]\n",
    "        raiz2 = fsolve(cu2,[guess])[0]\n",
    "        \n",
    "        # 1st order\n",
    "        if raiz != guess:\n",
    "        \n",
    "            b_raiz = B_fun(raiz)\n",
    "            b_list.append(b_raiz)\n",
    "            alpha_res.append(alpha)\n",
    "            \n",
    "        # 2nd order\n",
    "        if raiz2 != guess:\n",
    "        \n",
    "            b_raiz2 = B_fun(raiz2)\n",
    "            b_list2.append(b_raiz2)\n",
    "            alpha_res2.append(alpha)\n",
    "    \n",
    "    \n",
    "    # 1st order:\n",
    "    x = b_list*np.cos(alpha_res)\n",
    "    y = b_list*np.sin(alpha_res)\n",
    "    \n",
    "    if idx > 3:\n",
    "        x_interp = np.concatenate((y[-20:-10], y[10:20]))\n",
    "        y_interp = np.concatenate((-x[-20:-10], -x[10:20]))\n",
    "        f = interp1d(x_interp, y_interp, kind = 'quadratic')\n",
    "\n",
    "        x_new = np.linspace(y[-10], y[10], 100)\n",
    "        plt.plot(x_new, f(x_new), color = c,\n",
    "                    zorder = 1, lw = 4)\n",
    "        \n",
    "    #2nd order:\n",
    "    x2 = b_list2*np.cos(alpha_res2)\n",
    "    y2 = b_list2*np.sin(alpha_res2)\n",
    "    \n",
    "    ## Limits\n",
    "    xlims = [-32,32]\n",
    "    ylims = [-32,32]\n",
    "    \n",
    "    xplot = []\n",
    "    yplot = []\n",
    "        \n",
    "    for xp in x2:\n",
    "        if xlims[0] < xp < xlims[1]:\n",
    "            xplot.append(xp)\n",
    "            \n",
    "    for yp in y2:\n",
    "        if ylims[0] < yp < ylims[1]:\n",
    "            yplot.append(yp)\n",
    "    \n",
    "## Remove points\n",
    "    if abs(np.shape(xplot)[0] - np.shape(yplot)[0]) != 0:\n",
    "        \n",
    "        xshape = np.shape(xplot)[0] \n",
    "        yshape = np.shape(yplot)[0]\n",
    "        \n",
    "        if xshape < yshape:\n",
    "            dif = abs(np.shape(xplot)[0] - np.shape(yplot)[0]) \n",
    "\n",
    "            yplot2 = yplot[dif:]\n",
    "            xplot2 = xplot\n",
    "\n",
    "        if yshape < xshape:\n",
    "            dif = abs(np.shape(xplot)[0] - np.shape(yplot)[0]) \n",
    "\n",
    "            xplot2 = xplot[dif:]\n",
    "            yplot2 = yplot \n",
    "            \n",
    "          \n",
    "    plt.plot(y,-x,color = c,zorder = 2, lw = 4)\n",
    "    plt.plot(yplot2,xplot2,color = c, zorder = 1, lw = 4)\n",
    "\n",
    "# x_ovo = 3*M*np.cos(alpha_list)\n",
    "# y_ovo = 3*M*np.sin(alpha_list)\n",
    "\n",
    "# plt.plot(x_ovo,y_ovo)    \n",
    "circle = plt.Circle((0., 0.), 2*M, color='black', fill=True, zorder=0)\n",
    "plt.gca().add_patch(circle)\n",
    "circle = plt.Circle((0., 0.), 3*M, color='black', fill=True, zorder=0, alpha = 0.3)\n",
    "plt.gca().add_patch(circle)\n",
    "circle = plt.Circle((0., 0.), np.sqrt(3)*3*M, facecolor = 'none', edgecolor='white', fill=True,\n",
    "                    zorder=0, lw = 4)\n",
    "plt.gca().add_patch(circle)\n",
    "\n",
    "plt.xlim(-32,32)\n",
    "plt.ylim(-32,32)\n",
    "plt.axis('off')\n",
    "fig.patch.set_color('black')\n",
    "for ax in fig.axes:\n",
    "    ax.patch.set_color('black')\n",
    "plt.title(f'Relativistic Trilogy of Five', fontsize = 28,\n",
    "         color = 'white')\n",
    "fig.text(0.5, 0.1, f'Black Hole Photography', fontsize = 28,\n",
    "         color = 'white', ha = 'center')\n",
    "plt.savefig(f'Isoradical_theta_logo.png',\n",
    "            dpi = 300, bbox_inches = 'tight')\n",
    "plt.savefig(f'Isoradical_theta_logo.svg',\n",
    "            dpi = 300, bbox_inches = 'tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4425cce2-697f-423e-8612-34ca5be5efb9",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 50%|█████     | 1/2 [02:33<02:33, 153.73s/it]"
     ]
    }
   ],
   "source": [
    "for angle in tqdm([int(5*i) for i in range(17,19)]):\n",
    "    M = 1 # massa do BURACO negro\n",
    "    b_c = 3*np.sqrt(3)*M # parametro de impacto CRITICO\n",
    "    theta_0 = angle*np.pi/180. #angulo de visada do buraco negro\n",
    "\n",
    "    fig, ax = plt.subplots(figsize = (8,8))\n",
    "    #r_list = [30*M,20*M,10*M,6*M]\n",
    "    r_list = np.arange(4,30,0.5)*M\n",
    "    \n",
    "    color=iter(plt.cm.hot_r(np.linspace(0.3 ,1.,  np.shape(r_list)[0])))\n",
    "\n",
    "    for idx, r in enumerate(r_list):\n",
    "        if angle > 82:\n",
    "            alpha_list = np.arange(0, 4*np.pi,0.01)\n",
    "        else:\n",
    "            alpha_list = np.arange(0, 2*np.pi,0.01)\n",
    "        \n",
    "        c=next(color)\n",
    "        b_list = []\n",
    "        b_list2 = []\n",
    "        alpha_res = []\n",
    "        alpha_res2 = []\n",
    "        #plt.figure(figsize = (15,15), dpi = 300)\n",
    "        for alpha in alpha_list:    \n",
    "            # 1st order figure\n",
    "            def cu(P):\n",
    "                return 1 - r*Up(P,alpha)\n",
    "\n",
    "            # 2nd order figure\n",
    "            def cu2(P):\n",
    "                return -(1 - r*Up2(P,alpha))\n",
    "\n",
    "\n",
    "            guess = b_c + 0.1\n",
    "            # raiz = fsolve(cu,[guess])[0]\n",
    "            raiz = fsolve(cu,[guess])[0]\n",
    "            raiz2 = fsolve(cu2,[guess])[0]\n",
    "\n",
    "            # 1st order\n",
    "            if raiz != guess:\n",
    "\n",
    "                b_raiz = B_fun(raiz)\n",
    "                b_list.append(b_raiz)\n",
    "                alpha_res.append(alpha)\n",
    "\n",
    "            # 2nd order\n",
    "            if raiz2 != guess:\n",
    "\n",
    "                b_raiz2 = B_fun(raiz2)\n",
    "                b_list2.append(b_raiz2)\n",
    "                alpha_res2.append(alpha)\n",
    "\n",
    "\n",
    "        # 1st order:\n",
    "        x = b_list*np.cos(alpha_res)\n",
    "        y = b_list*np.sin(alpha_res)\n",
    "        if angle < 82:\n",
    "            if idx > 3:\n",
    "                x_interp = np.concatenate((y[-20:-10], y[10:20]))\n",
    "                y_interp = np.concatenate((-x[-20:-10], -x[10:20]))\n",
    "                f = interp1d(x_interp, y_interp, kind = 'quadratic')\n",
    "\n",
    "                x_new = np.linspace(y[-10], y[10], 100)\n",
    "                plt.plot(x_new, f(x_new), color = c,\n",
    "                            zorder = 1, lw = 4)\n",
    "\n",
    "        #2nd order:\n",
    "        x2 = b_list2*np.cos(alpha_res2)\n",
    "        y2 = b_list2*np.sin(alpha_res2)\n",
    "\n",
    "        ## Limits\n",
    "        xlims = [-32,32]\n",
    "        ylims = [-32,32]\n",
    "\n",
    "        xplot = []\n",
    "        yplot = []\n",
    "\n",
    "        for xp in x2:\n",
    "            if xlims[0] < xp < xlims[1]:\n",
    "                xplot.append(xp)\n",
    "\n",
    "        for yp in y2:\n",
    "            if ylims[0] < yp < ylims[1]:\n",
    "                yplot.append(yp)\n",
    "\n",
    "    ## Remove points\n",
    "        if abs(np.shape(xplot)[0] - np.shape(yplot)[0]) != 0:\n",
    "\n",
    "            xshape = np.shape(xplot)[0] \n",
    "            yshape = np.shape(yplot)[0]\n",
    "\n",
    "            if xshape < yshape:\n",
    "                dif = abs(np.shape(xplot)[0] - np.shape(yplot)[0]) \n",
    "\n",
    "                yplot2 = yplot[dif:]\n",
    "                xplot2 = xplot\n",
    "\n",
    "            if yshape < xshape:\n",
    "                dif = abs(np.shape(xplot)[0] - np.shape(yplot)[0]) \n",
    "\n",
    "                xplot2 = xplot[dif:]\n",
    "                yplot2 = yplot \n",
    "\n",
    "\n",
    "        plt.plot(y,-x,color = c,zorder = 2, lw = 4)\n",
    "        plt.plot(yplot2,xplot2,color = c, zorder = 1, lw = 4)\n",
    "\n",
    "    # x_ovo = 3*M*np.cos(alpha_list)\n",
    "    # y_ovo = 3*M*np.sin(alpha_list)\n",
    "\n",
    "    # plt.plot(x_ovo,y_ovo)    \n",
    "    circle = plt.Circle((0., 0.), 2*M, color='black', fill=True, zorder=0)\n",
    "    plt.gca().add_patch(circle)\n",
    "    circle = plt.Circle((0., 0.), 3*M, color='black', fill=True, zorder=0, alpha = 0.3)\n",
    "    plt.gca().add_patch(circle)\n",
    "    circle = plt.Circle((0., 0.), np.sqrt(3)*3*M, facecolor = 'none', edgecolor='white', fill=True,\n",
    "                        zorder=0, lw = 4)\n",
    "    plt.gca().add_patch(circle)\n",
    "\n",
    "    plt.xlim(-32,32)\n",
    "    plt.ylim(-32,32)\n",
    "    plt.axis('off')\n",
    "    fig.patch.set_color('black')\n",
    "    for ax in fig.axes:\n",
    "        ax.patch.set_color('black')\n",
    "    plt.title(f'Black hole accretion disk view - {int(theta_0*180/np.pi)}$^\\circ$', fontsize = 20,\n",
    "             color = 'white')\n",
    "    plt.savefig(f'Isoradical_theta_{int(theta_0*180/np.pi)}_mass_{int(M)}.png',\n",
    "                dpi = 300, bbox_inches = 'tight')\n",
    "    plt.savefig(f'Isoradical_theta_{int(theta_0*180/np.pi)}_mass_{int(M)}.svg',\n",
    "                dpi = 300, bbox_inches = 'tight')\n",
    "    plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4ec50446-bd22-4f37-8e9d-830db1a365d1",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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